I don't think the villain would value bet any worse hands than mine and if I check to him he will take the free showdown with pocket pairs Ahi hands and slowplayed 4. There aren't too many cards that could beat me, but some combos that could call me still exists. For instance if he had pocket jacks (he was passive so this is possible), he would certainly just check them but some of the time he could call my bet.

So what is the best line? Check/fold is too weak? Check/call valuetowns myself. Bet/call is kind of the same thing as check/call. Or just ship it?

Against the vast majority of players this would be a straightforward bet/call given the way the hand panned out, but if you think villain is only shoving a Ten here then I would bet 4.50 to get value against slowplayed 4 or PP and pukefold to shove.